Penrose's "Colchester Survey" of 1938 was the earliest serious attempt to study the genetics of mental retardation. He found that the relatives of patients with severe mental retardation were usually unaffected but some of them were affected with similar severity to the original patient, whereas the relatives of patients with mild mental retardation tended mostly to have mild or borderline disability. Penrose went on to identify and study many of the genetic and chromosomal causes of mental retardation (then called mental deficency). This remarkable body of work culminated in the classic book, The Biology of Mental Defect in 1949.

Penrose was a central figure in British medical genetics following World War II. From 1945 to 1965 he occupied the Galton Chair at the Galton Laboratory at University College, London. He received a number of awards and honors including the 1962 Albert Lasker Award for Basic Medical Research.[1], sometimes called "America's Nobel Prize." The Lasker citation read: "Professor Penrose and his associates have been responsible over the years for studies which touch all aspects of human genetics, include genetic analyses of most of the known hereditary diseases, contributions to mathematical genetics, biochemical genetics, the study of gene linkage in man, and theoretical work on the mutagenic effect of ionizing radiations. Most recently their attention has been turned to abnormalities of human chromosomes associated with congenital defects, particularly mongolism (Down syndrome)."

In British psychiatry, 'Penrose's Law' states that the population size of prisons and psychiatric hospitals are inversely related, although this is generally viewed as something of an oversimplification.

Penrose, a member of the Society of Friends (Quakers), was a lead figure in the Medical Association for the Prevention of War in the 1950s.

Penrose developed the Penrose method, a method for apportioning seats in a global assembly based on the square root of each nation's population.